Abstract
PERHAPS readers of NATURE will recognise the principle of the Eötvös torsion balance in the communication of Sir Arthur Schuster published in NATURE of October 20 (p. 240) entitled “The Tendency of Elongated Bodies to Set in the North and South Direction.” The calculation there given is, however, incomplete, and this causes the sign of the effect to be reversed. For the hypothetical “normal case” a complete calculation shows that the tendency is rather for an elongated body to set itself in an east and west direction. The missing element in the calculation is the difference in the directions of the centrifugal force on the different portions of the rod. If we call λ the longitude, reckoned from the meridian of the centre of the rod, of an element ds of the rod at distance s from the centre, then approximately λ = s sin ø/a sin θ, where a is the radius of the earth and the remaining notation is the same as in the original communication. Since λ is small, we may write for the horizontal force perpendicular to the meridian of the centre of the rod σρω2λds; its moment is (σρω2λds)(s cos ø), or, finally, since ρ = a sinθ, the moment of an element of length ds is σω2S2 sin ø cos ø ds.
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LAMBERT, W. The Tendency of Elongated Bodies to Set in the East and West Direction. Nature 108, 528 (1921). https://doi.org/10.1038/108528a0
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DOI: https://doi.org/10.1038/108528a0
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